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  1. #1
    Expert Forum User The Ultimate London Mom! eversoclever's Avatar
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    Default Test your thinking.

    When researchers put the following three problems to 3400 students in the US, only 17 per cent got all three right. Can you do any better?

    1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

    2) If it takes five machines 5 minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

    3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of it?

    Source: Journal of Economic Perspectives, Vol. 19

  2. #2
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    1. 5 cents
    2. 100 minutes
    3. 24

    answers? u can PM them to me if u wanna wait for lots of answers first, but I am curious now...
    Last edited by Mum09and11; 11-03-2009 at 12:43 AM.


  3. #3
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    Default

    .5
    100 minutes
    47 days

  4. #4
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    .05
    5
    47
    Last edited by strongmommy; 11-03-2009 at 06:00 AM.

  5. #5
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    .10
    100
    47

  6. #6
    Expert Forum User bacon's Avatar
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    I'm gonna get hurt on this one...

    5 cents?
    5 minutes?
    47 days?

  7. #7
    Expert Forum User The Ultimate London Mom!
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    5 cents
    5 minutes
    47 days

  8. #8
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    Quote Originally Posted by turtle View Post
    5 cents
    5 minutes
    47 days
    I agree with these answers ... my logic

    Bat and ball each cost a nickle which makes a dime - leaving the $1 left over

    Based on the 5 machines making 5 widgets in 5 minutes that meanst each widget takes 5 minutes to make so if a 100 machines are making 100 widgets they only need to make 1 widget each

    If the patch of lilies doubles it size each day on the 47th day half the lake is now covered as the 48th days doubling results results in the other half making a 'whole' coverage of the lake.

    Math AND logic first thing in the morning ... now I need chocolate to recover

  9. #9
    Expert Forum User le cupcake's Avatar
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    5 cents
    5 mins
    47 days
    mama to 3



  10. #10
    Expert Forum User The Ultimate London Mom! eversoclever's Avatar
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    So how many of you had to Google the answers? LOL!

    Visualizing #3 made me think of H1N1, heh.

    These three questions were first proposed by Shane Frederick of MIT and are commonly referred to as the “Cognitive Reflection Test” or the CRT. The questions basically test your reliance on logic vs. intuition and are supposedly correlated with one’s IQ and their willingness to wait for good things.

    Each question presents an easy “intuitive” answer which is actually incorrect. However, it is assumed that those with a higher IQ will notice that the intuitive answer contains inconsistencies that deserve a further (and more time consuming) examination. You might take it with a grain of salt, but it is interesting.

    The Solutions.

    For question #1, one might intuitively say, “$1.00 plus $0.10 is $1.10, therefore a ball costs $0.10“. While this is quite intuitive, it is also incorrect. A person who is more thorough might respond that the ball actually costs $0.05 (.05+(1+.05)=1.1). The correct answer is the ball costs $0.05.

    For question #2, an intuitive response would be that “5=5=5 so 100=100=100“. However, if it takes a single machine 5 minutes to make a single widget, even a million machines can make a million widgets in 5 minutes. The correct answer is therefore 5 minutes.

    For question #3, the common intuitive response would be, “half the pond would be covered in half the time, so 48/2=24 days“. However, this ignores the exponential growth of the lily pads. Try working it backwards, if the pond is covered after 48 days, and they double in size every day, then day 47 would be half covered. The correct answer is 47 days.

    How do you compare?

    How many did you get right? Compare your score to the below averages for various colleges.

    * Massachusetts Institute of Technology: 2.18
    * Princeton University: 1.63
    * Harvard University: 1.43
    * Web-based studies: 1.10
    * Michigan State University: 0.79

    Please note that even if you missed them all, don’t fret, it’s obviously not a full IQ test. I would imagine that getting each question is a bit like adding a few more points to an average IQ score. Besides, how much credence can you give some odd paper?

  11. #11
    Expert Forum User le cupcake's Avatar
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    I love these types of problems! I love working on them with kids to see how their brains solve problems. It's cool.
    mama to 3



  12. #12
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    Alright Clevs, trying my hand...

    When researchers put the following three problems to 3400 students in the US, only 17 per cent got all three right. Can you do any better?

    1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

    5 cents?

    2) If it takes five machines 5 minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

    5 minutes?

    3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of it?

    Uhhh... 24 days? That's probably wrong LOL.

  13. #13
    Expert Forum User The Ultimate London Mom!
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    Quote Originally Posted by eversoclever View Post
    For question #3, the common intuitive response would be, “half the pond would be covered in half the time, so 48/2=24 days“. However, this ignores the exponential growth of the lily pads. Try working it backwards, if the pond is covered after 48 days, and they double in size every day, then day 47 would be half covered. The correct answer is 47 days.
    Ahh geez.

  14. #14
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    Seeing as how many of us got a lot right, I wonder if the Princeton grads et al are just conceited? I know I would have been tripped up on all three except I kept thinking 'that's gotta be too easy.'

  15. #15
    Expert Forum User The Ultimate London Mom! eversoclever's Avatar
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    Quote Originally Posted by myrrah View Post
    Seeing as how many of us got a lot right, I wonder if the Princeton grads et al are just conceited? I know I would have been tripped up on all three except I kept thinking 'that's gotta be too easy.'
    I know! I kept thinking to myself, well at least I know I'm a dumbshit.

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